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SIMDized cluster transformation for ALICE HLT

SIMDized cluster transformation for ALICE HLT. S ergey Gorbunov. ALICE HLT: Reconstruction in TPC tracker . TPC sector 0. TPC sector 35. . The Cluster Transformation applies calibration and alignment to the TPC clusters. It was the show stopper for HLT:

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SIMDized cluster transformation for ALICE HLT

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  1. SIMDized cluster transformation for ALICE HLT SergeyGorbunov

  2. ALICE HLT: Reconstruction in TPC tracker TPC sector 0 TPC sector 35  The Cluster Transformation applies calibration and alignment to the TPC clusters. It was the show stopper for HLT: • off-line code under development, • speed is out of the HLT control • getting more and more complicated • suddenly became 10 times slower FPGA Cluster Finder Cluster Finder  CPU, slow Cluster Transformation Cluster Transformation  GPU SectorTracker SectorTracker  CPU, fast TPC trackmerger Sergey Gorbunov, FIAS

  3. ALICE HLT: Transformation of TPC clusters TPC sector TPC cluster transformation: (Pad, Time)->(X,Y,Z) rowk Time bin Row number -> X Pad -> Y Time -> Z t9 t0 p0 p1 Readout pads Sergey Gorbunov, FIAS

  4. ALICE HLT: New composed transformation Composed TPC transformation: 1. TPCExBShape 2. alignGlobal 3. alignLocal 4. alignQuadrant 5. FCVoltError3D 6. FitBoundary 7. FitExBTwist 8. FitAlignTPC 9. FitRocAlignZSum … there will be more Speed: 7.9 ms/cluster = 6 s/event (PbPb) Toomany different transformations – nohopetooptimizethecode ... Sergey Gorbunov, FIAS

  5. ALICE HLT: Cluster transformation for particular TPC pad Final transformation:It does not look that complicated: X zoomed X Sec=0, Row=0, pad coordinate in [30,31] Y Z Sergey Gorbunov, FIAS

  6. ALICE HLT: Fast transformation Idea:Fit the original Transformation with polynoms/splines: Initialization phase: Create temporary splines by calling TPCTransform() : - no matter which corrections are applied, - no matter how slow it is Running phase: Use of the splines: - few arithmetic operators --- very fast - transformation time is constant: no more dependence on other code and data base objects Sergey Gorbunov, FIAS

  7. ALICE HLT: Fast transformation Idea:Fit the original Transformation with polynoms/splines: Requirements: • Accuracy: 100 um • Speed: 10 times faster • Transformation for 33 rows should fit to CPU cache • Use of SIMD vectors (Vc package) for faster calculations Size of cluster, Y Size of cluster, Z Sergey Gorbunov, FIAS

  8. ALICE HLT: Fast transformation: Polynomial fit Fit with polynoms:Many local features- does not work well: Difference with polynom of 0 order [cm]: X Z Y Difference with 5-th order polynom [cm]: Y X Z Sergey Gorbunov, FIAS

  9. ALICE HLT: Fast transformation: Fit with splines Fit with splines:Accuracy about 0.1 um for X,Y,Z X Worst deviation in X: 88um, in Y: 81um, in Z: 3.8um Sergey Gorbunov, FIAS

  10. ALICE HLT: Fast transformation Fast HLT transformation:TPC row with the worst deviations (Orig. - Fast transformation)[um] vs Pad and Time Sergey Gorbunov, FIAS

  11. ALICE HLT: Fast transformation Fast HLT transformation:TPC row with the worst deviations Original X vs pad Original Y vs pad 140 um gap 120 um gap This particular TPC row seems to be miscalibrated to 140um -> accuracy of the Fast Transformation [80um] here is not worse than the accuracy of the original transformation [140um]. Sergey Gorbunov, FIAS

  12. ALICE HLT: Parallel algorithm (Cellular Automaton) Fast HLT Transformation:Results • Accuracy: 0.1 um • Speed-up in scalar: 58.1 times • Speed-up with SIMD vectors: 83.6 times • (SIMD give factor 1.44 extra speed-up) • Transformation size for 33 rows: 170kB ( full TPC: 29MB) Use of SIMD vectors: • Vc package from M.Kretz – very useful tool • Spline points are stored as 4-vectors: (x,y,z,*) • This scheme allows one to avoid packing of data to vectors, but it only works with SIMD vectors of size 4. Sergey Gorbunov, FIAS

  13. ALICE HLT: Summary • Parallelization in ALICE HLT: • All time-consuming HLT components are running • now on parallel hardware: • cluster finder: FPGA • cluster transformation: SIMD (via Vc package) • sector tracker: GPU • Fast transformationgivesfactorof83.6timesspeed-up • Vcpackageinstalledandcanbeused offline aswell Sergey Gorbunov, FIAS

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